One way is to create the hash differently. Only keep the 1st 3 letters of File1 as the keys. Then, grab the 2nd column of File2 and, again, only use the 1st 3 letters.

use strict;
use warnings;

my ($f1,$f2,%patts,$f2_rec,$f2_field);
$f1 = $ARGV[0];
$f2 = $ARGV[1];

open(PATT,"<", $f1) or die;
while (<PATT>) {
    chomp;
    $patts{substr $_, 0, 3} = 1;
}
close(PATT) or die;

open(FILE,"<", $f2) or die;
while (defined ($f2_rec = <FILE>))
{
    chomp $f2_rec;
    $f2_field = (split(/ /,$f2_rec))[1];
    $f2_field = substr $f2_field, 0, 3;
    if(exists($patts{$f2_field}))
    {
        print "$f2_rec\n";
    }
}
close(FILE) or die;
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